A Genetic Algorithm Approach to Identification of Nonlinear Polynomial Models

Abstract In the last two decades, linear-in-parameter nonlinear polynomial models for NARX (Nonlinear Auto-Regressive with eXogenous input) systems have received considerable attention. The keypoint of polynomial model identification is how to select a set of significant terms employed to approximate the NARX system under study, from a large number of candidates. To this end, the orthogonal least-squares method which is a local search procedure, and the genetic algorithm approach which has a high potential for global optimization have been proposed in the literature. However, it is considered that the methods reported so far in the literature still lack potential to identify the polynomial models with relatively high-order. This limits the applicability of the polynomial models to the real complex nonlinear systems. Motivated by this fact, in this paper, a new genetic algorithm approach to polynomial model identification is proposed. Our contribution in this paper is to introduce a novel hierarchical encoding technique which is considered to be suitable to the structure of the polynomial models. Simulation and application results are also included to verify the efficiency of the proposed identification algorithm.